If the number of bellows elements is made double and the thickness of the bellows element is made half, the displacement of the element for the same applied pressure would be the _______.

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SSC JE EE Previous Year Paper 17 (Held On: 4 March 2017 Evening)
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  1. 16 times
  2. 4 times
  3. same
  4. one-fourth

Answer (Detailed Solution Below)

Option 1 : 16 times
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Concept:

A metallic bellow is a series of circular parts, resembling the folds in an accordion. These parts are formed or joined in such a manner that they expanded or contracted axially.

The displacement of the bellows element is given by

\(d=\frac{0.453~Pbn{{D}^{2}}\sqrt{1-{{\nu }^{2}}}}{E{{t}^{3}}}\)  

Where P = pressure in N/m2

b = radius of each corrugation

n = thickness of the wall in m

D = mean diameter, m

E = modulus of elasticity, N/m2

ν = Poisson’s ration

Calculation:

\(d\propto \frac{n}{{{t}^{3}}}\)

n made double and t made half, hence displacement becomes 16 times.
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